Coaching and SAT scores: Critique $(4.1,4.3)$ The data you used in the previous two exercises came from a random sample of students who took the SAT twice. The response rate was $63\%$, which is pretty good for nongovernment surveys.

(a) Explain how nonresponse could lead to bias in this study.

(b) We can’t be sure that coaching actually caused the coached students to gain more than the un-coached students. Explain briefly but clearly why this is so

The response rate was $63\%$, which is pretty good for nongovernment surveys.

The people who responded might have a very different result than those who did not respond. For example, people with very low scores will most likely be to embarrassed to respond.

Since the scores of the nonresponses could be very different from the scores of the responders, the true values and conclusions might be very different for the two groups.

Thus the results cannot be generalized to the entire population.

The response rate was $63\%$, which is pretty good for nongovernment surveys.

Individuals are purposely subjected to a treatment in order to examine their reactions in an experiment.

An observational study tries to gather information without disturbing the scene they are observing.